Analyzing numerically study the effect of add a spacer layer in gires tournois

International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 –
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME
85
ANALYZING NUMERICALLY STUDY THE EFFECT OF ADD A
SPACER LAYER IN GIRES-TOURNOIS INTERFEROMETER DESIGN
Gaillan H. Abdullah 1
, Elham Jasim Mohammad 2
1
Physics Directorate, Technology Materials Chemistry/Ministry of Science, Iraq
2
Physics Department, Collage of Sciences/Al-Mustansiriyah University, Iraq
ABSTRACT
We demonstrated Gires-Tournoise interferometer (GTI) design as an optical standing-
wave cavity to generate chromatic dispersion. In this research we design three structures with
different spacers to study the impact on the pulse width and reflectivity using two types of
dielectric materials TiO2/SiO2 as the high and low refractive index.
Keywords: Gires-Tournoise, Group Delay Dispersion, Optical Filter, Round Trip.
I. INTRODUCTION
Optical filters have been widely applied to optical communication systems and fiber
sensing fields. With the rapid development of optical communication, many techniques have
been proposed for optical filters, such as birefringence, optical-electric thin-films, array
waveguide gratings, ring resonators, fiber gratings, Michelson and Mach-Zehnder
interferometers, and Gires-Tournois interferometer (GTI) [1].
Gires-Tournois interferometers are generally used to compensate highly chirped
picosecond or femtosecond pulses the way they exist, especially in narrow gain band-width
lasers like Nd: YAG. Large amounts of intracavity negative GDD are essential in ultrashort
pulse lasers, in order to compensate for the gain bandwidth and self-phase modulation (SPM)
due to nonlinear elements [2]. In comparison to a prism pair sequence, the GTI is easily three
orders of magnitude more dispersive but also linear over a much smaller bandwidth. The
amount of available group delay dispersion can be further increased by reecting the
intracavity pulse several times of the surface of the GTI, because the introduced dispersion is
proportional to the number of bounces from the surface. Several schemes of GTI have been
proposed introducing these large amounts of group delay dispersion (GDD) [3]. In large gain
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bandwidth lasers like Ti:sapphire and Cr:LiSAF the GTI are used to tune the laser in the
picosecond regime. This is done by changing the pulse angle of incidence upon the GTI,
which thereby correctly compensates a narrow bandwidth of intracavity dispersion [4]. So
far, these devices have been used in a much ex-perimental manner, by simply maintaining the
round trip time inside the GTI much below the pulse duration and adjusting the number of
reactions from its surface in order to minimize the pulse duration. Here we calculate the
bandwidth over which the dispersion of a GTI is linear. We are therefore capable of
designing a GTI, which introduces constant GDD over the whole gain bandwidth (FWHM),
meanwhile keeping the losses low by minimizing the number of reactions needed [4,5].
II. GTI THEORY AND PRINCIPLE OF OPERATION
A Gires-Tournois interferometer consists of two parallel surfaces, the second of which
is 100 % reflective as show in Figure 1. Therefore, the two quantities which characterize the
GTI are the reflection coefficient r of the first surface and the distance ݀ between them [6].
Figure 1: Schematic setup of a gires–tournois interferometer [7]
The round trip time inside the GTI for an angle of incidence ߠ is then given by [4]:
‫ݐ‬଴ ൌ
ଶ௡ௗ
௖
ට1 െ
௦௜௡మఏ
௡మ (1)
Where c is the speed of light and ݊ the refractive index of the medium between the
mirrors. If the pulse duration is longer than t0, the fields of successive reflections of the same
pulse do temporally overlap and the pulse envelope may be reshaped. This puts an upper limit
to the distance between the reecting surfaces. But, as the distance d becomes shorter, the
GDD becomes smaller too, as can be seen from the equation below [4]:
‫ܦܦܩ‬ ൌ 2ߨ
ௗ்
ௗఠ
ൌ െ2ߨ
ௗమ‫׎‬
ௗఠమ ൌ 2ߨ‫ݐ‬ଶ
ଶ ൫௥మିଵ൯ଶ௥ ୱ୧୬ ఠ௧బ
ሺଵା௥మିଶ௥ ୡ୭ୱ ఠ௧బሻమ (2)
where, T = group delay , ߱=angular frequency, ‫=׎‬ phase and r= reflectivity.
In order to obtain constant negative GDD over finite bandwidth, ω > 0, the phase
has to be adjusted such that the GDD is a minimum. This phase is a function of r, as seen in
above equation. In order to obtain high values of negative dispersion and large bandwidth

87
(for short pulse duration), one has to increase the reflectivity of the intermediate mirror in a
controlled manner. The commonly used round trip time (1) shows no dependency with the
intermediate surface reflectivity. We know, that the higher the reflectivity, the longer the
delay time within the GTI. Therefore, as the reflectivity increases, the pulse, coming out of
the GTI, gets stretched in time. Taking into account the reflectivity we derive an expression
for the decay time of a pulse in a passive resonator, τ [4]:
߬ ൌ ‫ݐ‬଴ . ቜ1 ൅
ଵ
୪୬ቀଵ
௥మൗ ቁ
ቝ (3)
Where t0 is given by (1). By analyzing numerically various GTI's we found that this
expression gives a very good estimate in the case of Fourier transform limited pulse width. A
more useful approximation is obtained by calculating the bandwidth, ∆νGTI, over which the
group delay is linear. We therefore expand the group delay as a function of frequency about
the points of maximum GDD. At these points the second derivative of the group delay is zero
and we obtain [8]:
ܶሺ߱ሻ ൌ ܶሺ߱଴ሻ ൅
ௗ்ሺఠబሻ
ௗఠ
∆߱ ൅
ௗయ்ሺఠబሻ
଺ௗఠయ ∆߱ଷ
(4)
Linearity of the group delay is guaranteed as long as the third term in above equation is
smaller than the second term [8]:
ௗ்ሺఠబሻ
ௗఠయ ൌ
ௗ்ሺఠబሻ
ௗఠ
∆߱ (5)
Where we have dropped the factor (6) in the denominator of the third term. Using the above
criteria for linearity we obtain:
∆νGTI ൌ 2
∆ఠ
ଶగ
ൌ
ଵ
గ
ටௗ்ሺఠబሻ
ௗఠ
ቀ
ௗయ்ሺఠబሻ
ௗఠయ ቁ
ିଵ
(6)
III. DESIGN AND DISCUSSION
Since in 1984~1987, whereas standard quarter-wave dielectric mirrors were shown to
introduce negligible dispersion at the center of their reflectivity bands [9-11], various specific
high-reflectivity coatings (GTI, double-stack mirrors, etc.) with adjustable GDD (through
angle tuning) were devised and used for the precise control of intra-cavity dispersion in
femtosecond dye lasers. The material used in all design is TiO2/SiO2 as the high and low
refractive index. The design wavelength is 600nm and the spectral range 450–800nm.
Figure 2 and Figure 3 show the reflectance and reflectance GDD, where H and L are quarter
wave layers at 800nm with indices 2.35 and 1.45 which correspond to TiO2 and SiO2,
respectively, and the refractive index of Glass is 1.51. The bandwidth of high reflectance
(>70%) is 520~710 nm, and the reflectance GDD value is near zero. Table 1 shows the layer
structure for the first design.

International Journal of Advanced Research in Engineering and Technology (IJARET),
6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March
Figure 2: Ref
Figure 3: Group delay dis
Table 1
No Materials
Thicknesses
1 TiO2
2 SiO2
3 TiO2
4 SiO2
5 TiO2
Then we add a spacer 2H and a low reflectance st
reflectance and reflectance GDD of the stack are showing in
shows Layer structure of the second
Figure 4: Reflection vs. wavelength
6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME
88
eflections vs. wavelength for the first design
roup delay dispersion vs. wavelength for the first design
Table 1: Layer structure of the first design
Thicknesses
(nm)
No. Materials
Thicknesses
(nm )
64.844 6 SiO2 101.303
101.303 7 TiO2 64.844
64.844 8 SiO2 101.303
101.303 9 TiO2 64.844
64.844 10 SiO2 101.844
Then we add a spacer 2H and a low reflectance stack (LH) to the above design
reflectance and reflectance GDD of the stack are showing in Figure 4 and Figure
second design.
eflection vs. wavelength for the second design
April (2013), © IAEME
design
Thicknesses
ack (LH) to the above design, the
Figure 4 and Figure 5. Table 2

6480(Print), ISSN 0976 – 6499(Online) Volume 4, Issue 2, March
Table 2:
No Materials Thicknesses
1 TiO2
2 SiO2
3 TiO2
4 SiO2
5 TiO2
6 SiO2
7 TiO2
The reflectance is broading
GDD has a high non-linear value in the bandwidth of 570~620nm.
Finally, if the spacer 2H in Figure
third design shows in Table 3.
Figure 6: Reflection vs. wavelength for third
6499(Online) Volume 4, Issue 2, March – April (2013), © IAEME
89
roup delay dispersion vs. wavelength for the second design
Layer structure for the second design
Thicknesses
(nm)
No. Materials Thicknesses
(nm )
64.844 8 SiO2 101.303
101.303 9 TiO2 64.844
64.844 10 SiO2 101.844
101.303 11 TiO2 129.689
64.844 12 SiO2 101.303
101.303 13 TiO2 64.844
64.844
The reflectance is broading from 190nm to 230 nm (510~740nm), but the reflectance
linear value in the bandwidth of 570~620nm.
Finally, if the spacer 2H in Figure 4 changed to 10H, then the Layer structure of
Reflection vs. wavelength for third design
roup delay dispersion vs. wavelength for the third design
April (2013), © IAEME
design
Thicknesses
but the reflectance
Layer structure of the
design

90
Table 3: Layer structure of the third design
(nm)
(nm )
1 TiO2 64.844 7 TiO2 64.844
2 SiO2 101.303 8 SiO2 101.303
3 TiO2 64.844 9 TiO2 64.844
4 SiO2 101.303 10 SiO2 101.844
5 TiO2 64.844 11 TiO2 713.289
6 SiO2 101.303 12 SiO2 101.303
From Figure 6 and Figure 7, it is clearly seen that the values of the reflectance and
reflectance GDD is becoming higher than the one in Figure 4. But the bandwidth of high
reflectance is narrow and the non-linear reflectance GDD is worse than the one in Figure 5.
IV. CONCLUSION
A Gires–Tournois interferometer is an optical standing-wave resonator designed for
generating chromatic dispersion. The front mirror is partially reflective, whereas the back
mirror has a high reflectivity. If no losses occur in the resonator, the power reflectivity is
unity at all wavelengths, but the phase of the reflected light is frequency-dependent due to the
resonance effect, causing chromatic dispersion. The phase change of reflected light and the
dispersion (including group delay dispersion and higher-order dispersion) change periodically
with optical frequency, if material dispersion is negligible. There is no second-order
dispersion exactly on-resonance or anti-resonance, and positive or negative dispersion
between these points.
Ideally, the GTI is operated near a maximum or minimum of the GDD, and the usable
bandwidth is some fraction (e.g. one-tenth) of the free spectral range, which is inversely
proportional to the resonator length. In the time domain, this means that the pulse duration
needs to be well above the round-trip time of the GTI. The maximum magnitude of GDD
scales with the square of the resonator length.
From the above result, we can see that the layer structure can be easily adapted for any other
wavelength regime. We believe that this compensator of thin-film has more potential to be
deployed in ultrafast optics and optical communication.
REFERENCES
[1] Y. Zhang, W. Huang, X. Wang, H. Xu, Z. Cai, A novel super-high extinction ratio
comb-filter based on cascaded Mach-Zehnder Gires-Tournois interferometers with
dispersion Compensation, OSA, 17(16), 2009, 13685-13699.
[2] E. P. Ippen, Principles of Passive mode Locking, Appl. Phys B 58, 1994, 159.
[3] J. Kuhl, J. Heppner, Compression of Femtosecond Optical Pulses with Dielectric
Multilayer Interferometers, IEEE J. Quant. Electron. QE- 22, 1986, 182.
[4] J. D. Kafka, M. L. Watts, J-W. J. Pieterse, Picosecond and Femtosecond Pulse
Generation in a Regeneratively Mode-Locked Ti:Sapphire Laser, IEEE J. Quant.
Electron. QE-28, 1992, 2151.

91
[5] R. Szipıcs, Dispersive Properties of Dielectric Laser Mirrors and their Use in
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[6] L. Orsila, Interferometric Dielectric Reflectors for Dispersion Compensation in Fiber
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[7] http://www.rp-photonics.com/gires_tournois_interferometers.html.
[8] M. Ramaswamy, A.S. Gouveia-Neto, D.K. Negus, J.A. Izatt and J.G. Fujimoto, 2.3-ps
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[9] W. Dietel, E. Dbpel, K. Hehl, W. Rudolph, and E. Schmidt, Multilayer dielectric mirrors
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[11] W. H. Knox, N. M. Pearson, K D. Li, and Ch. A. Hirlimann, Interferometric
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[12] K. Karuna Kumari and Dr. P.V.Sridevi, “Performance Evaluation of Circular Microstrip
Patch Antenna Array with Different Dielectric Substrate Materials”, International
journal of Electronics and Communication Engineering &Technology (IJECET),
Volume 4, Issue 1, 2013, pp. 236 – 249, ISSN Print: 0976-6464, ISSN Online: 0976-6472.
[13] Ahmed Thabet and Youssef A. Mobarak, “Experimental Study for Dielectric Strength of
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ISSN Print : 0976-6545, ISSN Online: 0976-6553.

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